Multilinear subspace learning

Multilinear subspace learning is an approach to dimensionality reduction.Dimensionality reduction can be performed on data tensor whose observations have been vectorized and organized into a data tensor, or whose observations are matrices that are concatenated into a data tensor. Here are some examples of data tensors whose observations are vectorized or whose observations are matrices concatenated into data tensor images (2D/3D), video sequences (3D/4D), and hyperspectral cubes (3D/4D).

The mapping from a high-dimensional vector space to a set of lower dimensional vector spaces is a multilinear projection.

Multilinear subspace learning algorithms are higher-order generalizations of linear subspace learning methods such as principal component analysis (PCA), independent component analysis (ICA), linear discriminant analysis (LDA) and canonical correlation analysis (CCA).

With the advances in data acquisition and storage technology, big data (or massive data sets) are being generated on a daily basis in a wide range of emerging applications. Most of these big data are multidimensional. Moreover, they are usually very-high-dimensional, with a large amount of redundancy, and only occupying a part of the input space. Therefore, dimensionality reduction is frequently employed to map high-dimensional data to a low-dimensional space while retaining as much information as possible.

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